Modern chemotherapy cures the majority of patients with Hodgkin's disease and intermediate grade non-Hodgkin's lymphomas. However, standard dose chemotherapy is rarely curative for patients who fail to achieve a complete remission to induction chemotherapy or whose initial complete remission lasts less than 12 months. High-dose chemotherapy and autologous bone marrow transplantation have been able to achieve longer lasting complete remissions in some of these patients. There is a clear need for improving the rates at which bone marrow and peripheral blood counts recover following the myeloablative regimens used in these treatments. In this study, patients with Hodgkin's and non-Hodgkin's lymphoma are debulked with combination chemotherapy. Those patients achieving a complete remission, or 90% partial remission, receive high- dose chemotherapy with the ICE (ifosfamide, carboplatin, etoposide) regimen. As a source of stem cells, both bone marrow and peripheral blood will be used. Prior to harvesting peripheral blood and bone marrow, patients will receive IL-1beta and G-CSF. Following high-dose chemotherapy and these stem cells, patients will receive additional G-CSF. Still only six patients have been registered. One patient was not enrolled because of bone marrow involvement with lymphoma; two patients died from treatment-related toxicity and three patients achieved a complete remission. Two patients with Hodgkin's disease remain in CR at 3+ and 2+ years. One patient with non-Hodgkin's lymphoma relapsed from CR lasting 2 years and is currently undergoing therapy.